Abstract
The standard treatment of orthogonal polynomials is Szegö (1958), in which several other systems are described and more properties of orthogonal polynomials are discussed. A general reference on multivariate orthogonal polynomials is Dunkl and Yu (2001). A type of orthogonal system that I mentioned, but did not discuss, are wavelets. For this I refer the reader to Walter and Ghorai (1992) or to Vidakovic (2004).
De Boor (2002) provides a comprehensive development of splines and an extensive discussions of their properties. The emphasis is on B-splines and he gives several Fortran routines for using B-splines and other splines. A good introduction to multivariate splines is given by Chui (1988).
Evans and Schwartz (2000) provide a good summary of methods for numerical quadrature, including both the standard deterministic methods of numerical analysis and Monte Carlo methods. The most significant difficulties in numerical quadrature occur in multiple integration. The papers in the book edited by Flournoy and Tsutakawa (1991) provide good surveys of specific methods, especially ones with important applications in statistics.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer-Verlag New York
About this chapter
Cite this chapter
Gentle, J.E. (2009). Approximation of Functions and Numerical Quadrature. In: Computational Statistics. Statistics and Computing. Springer, New York, NY. https://doi.org/10.1007/978-0-387-98144-4_4
Download citation
DOI: https://doi.org/10.1007/978-0-387-98144-4_4
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98143-7
Online ISBN: 978-0-387-98144-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)